FIRST BROWNLEE 4 3 E1 1 12161 3111 EX1 0010
( A6, I4, I2, 2F6.3, F5.2, F1.0, F6.3, 2F1.0 ) EX1 0011
22 EX1 0012
23 4 EX1 0013
1 2 3 4 2 61 8 -2. 71 6 100. 7 EX1 0020
EXAMPLE OF SAVING COEFFICIENTS FOR CROSS VERIFICATION OF EQUATION, EX1 0030
REDUCING PRINTOUT (CENTRAL RESIDUALS AND OBSERVATIONS 10-12), E FORMAT, EX1 0040
DELETED OBSERVATION, INDICATOR-VARIABLE-OBSERVATION, AND CP FACTORIAL EX1 0041
SEARCH WITH GIVEN ESTIMATE OF VARIANCE. EX1 0050
OBSERVATION 22 DELETED FROM FIRST SET OF DATA, INCLUDED IN NEXT SET. EX1 0060
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 EX1 0070
Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES EX1 0080
IN THE 55 TO 59 AGE GROUP) - 2 ) EX1 0090
X1 = 1000(TELEPHONES PER PERSON) EX1 0100
X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES EX1 0110
X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES EX1 0120
X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE. EX1 0121
TELEPH F. CAL AP.CAL UN IND DEATHS EX1 0130
1 2 3 EX1 0131
AUSTRL 1 124 33 8 646 EX1 0140
ASTRIA 2 49 31 6 355 EX1 0150
CANADA 3 181 38 8 631 EX1 0160
CEYLON 4 4 17 2 174 EX1 0170
CHILE 5 22 20 4 603 EX1 0180
DENMK 6 152 39 6 331 EX1 0190
FINLND 7 75 30 7 759 EX1 0200
FRANCE 8 54 29 7 282 EX1 0210
GMANY 9 43 35 6 316 EX1 0220
IRELND 10 41 31 5 490 EX1 0230
ISRAEL 11 17 23 4 457 EX1 0240
ITALY 12 22 21 3 282 EX1 0250
JAPAN 13 16 8 3 174 EX1 0260
MEXICO 14 10 23 3 269 EX1 0270
NTHLDS 15 63 37 6 240 EX1 0280
NWZEAL 16 170 40 8 525 EX1 0290
NORWAY 17 125 38 6 257 EX1 0300
PORTGL 18 15 25 4 240 EX1 0310
SWEDEN 19 221 39 7 331 EX1 0320
SWITZD 20 171 33 7 331 EX1 0330
UNKING 21 97 38 6 457 EX1 0340
U.S.A. 22 254 39 8 776 EX1 0341
U.N. 23 87 30 5 776 EX1 0342
END EX1 0350
235. EX1 0351
NEXT BROWNLEE 4 3 1 1 101 2 1 EX1 0360
( A6, I4, I2, 2F6.3, F5.2, F1.0, F6.3, 2F1.0 ) EX1 0361
23 4 EX1 0362
1 2 3 4 2 61 8 -2. 71 6 100. 7 EX1 0370
EXAMPLE OF CROSS VERIFICATION WITH SAVED COEFFICIENTS FROM FIT WITH EX1 0371
FIRST SET OF DATA. THIS SECOND SET OF DATA CONTAINS USA, OBSERVATION EX1 0372
22, DELETED FROM FIRST SET OF DATA. EX1 0373
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 EX1 0380
Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES EX1 0390
IN THE 55 TO 59 AGE GROUP) - 2 ) EX1 0400
X1 = 1000(TELEPHONES PER PERSON) EX1 0410
X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES EX1 0420
X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES EX1 0430
X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE. EX1 0431
TELEPH F. CAL AP.CAL UN IND DEATHS EX1 0440
AUSTRL 1 124 33 8 646 EX1 0450
ASTRIA 2 49 31 6 355 EX1 0460
CANADA 3 181 38 8 631 EX1 0470
CEYLON 4 4 17 2 174 EX1 0480
CHILE 5 22 20 4 603 EX1 0490
DENMK 6 152 39 6 331 EX1 0500
FINLND 7 75 30 7 759 EX1 0510
FRANCE 8 54 29 7 282 EX1 0520
GMANY 9 43 35 6 316 EX1 0530
IRELND 10 41 31 5 490 EX1 0540
ISRAEL 11 17 23 4 457 EX1 0550
ITALY 12 22 21 3 282 EX1 0560
JAPAN 13 16 8 3 174 EX1 0570
MEXICO 14 10 23 3 269 EX1 0580
NTHLDS 15 63 37 6 240 EX1 0590
NWZEAL 16 170 40 8 525 EX1 0600
NORWAY 17 125 38 6 257 EX1 0610
PORTGL 18 15 25 4 240 EX1 0620
SWEDEN 19 221 39 7 331 EX1 0630
SWITZD 20 171 33 7 331 EX1 0640
UNKING 21 97 38 6 457 EX1 0650
U.S.A. 22 254 39 8 776 EX1 0660
U.N. 23 87 30 5 776 EX1 0661
END EX1 0670
MANDEL WEIGHT OBSV 1 1 1 1 51 EX2 0010
SAMPLE LEVEL OF X WEIGHT OF OBSERVATION EX2 0020
1 10 1 EX2 0030
2 20 4 EX2 0040
3 30 1 EX2 0050
4 40 1 EX2 0060
LEVEL EX2 0070
1 10. 33.8 1. EX2 0080
2 20. 62.2 4. EX2 0090
3 30. 92.0 1. EX2 0100
4 40. 122.4 1. EX2 0110
END EX2 0120
PRECISION - EMPLOY 6 8 1 1111 1 11 812 2 EX3 0010
( A6,I4,I2, F6.1,9F6.0/ 12X, 4F6.0 ) EX3 0020
1 2 3 4 5 6 7 EX3 0030
81 91 101 111 121 131 141 EX3 0040
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 + B(5)X5 + B(6)X6 EX3 0050
Y = EMPLOYMENT EX3 0060
X1 = PRICE INDEX EX3 0070
X2 = GROSS NATIONAL PRODUCT EX3 0080
X3 = UNEMPLOYMENT EX3 0090
X4 = SIZE OF ARMED FORCES EX3 0100
X5 = NONINSTITIONAL POPULATION EX3 0110
X6 = TIME IN YEARS EX3 0120
PRICE GNP UNEMPY ARMY NONIST TIME TOTAL EX3 0130
FARM SELF UNPAID HOUSE PRIVAT FED GOV LOCALG EX3 0140
JASA P1947 1 83.0234289 2356 1590107608 1947 60323 8256 6045 427EX3 0150
JASA 1947 2 1714 38407 1892 3582 EX3 0160
JASA R1948 1 88.5259426 2325 1456108632 1948 61122 7960 6139 401EX3 0170
JASA 1948 2 1731 39241 1863 3787 EX3 0180
JASA E1949 1 88.2258054 3682 1616109773 1949 60171 8017 6208 396EX3 0190
JASA 1949 2 1772 37922 1908 3948 EX3 0200
JASA C1950 1 89.5284599 3351 1650110929 1950 61187 7497 6069 404EX3 0210
JASA 1950 2 1995 39196 1928 4098 EX3 0220
JASA I1951 1 96.2328975 2099 3099112075 1951 63221 7048 5869 400EX3 0230
JASA 1951 2 2055 41460 2302 4087 EX3 0240
JASA S1952 1 98.1346999 1932 3594113270 1952 63639 6792 5670 431EX3 0250
JASA 1952 2 1922 42216 2420 4188 EX3 0260
JASA I1953 1 99.0365385 1870 3547115094 1953 64989 6555 5794 423EX3 0270
JASA 1953 2 1985 43587 2305 4340 EX3 0280
JASA O1954 1 100.0363112 3578 3350116219 1954 63761 6495 5880 445EX3 0290
JASA 1954 2 1919 42271 2188 4563 EX3 0300
JASA N1955 1 101.2397469 2904 3048117388 1955 66019 6718 5886 524EX3 0310
JASA 1955 2 2216 43761 2187 4727 EX3 0320
JASA 1956 1 104.6419180 2822 2857118734 1956 67857 6572 5936 581EX3 0330
JASA 1956 2 2359 45131 2209 5069 EX3 0340
JASA T1957 1 108.4442769 2936 2798120445 1957 68169 6222 6089 626EX3 0350
JASA 1957 2 2328 45278 2217 5409 EX3 0360
JASA E1958 1 110.8444546 4681 2637121950 1958 66513 5844 6185 605EX3 0370
JASA 1958 2 2456 43530 2191 5702 EX3 0380
JASA S1959 1 112.6482704 3813 2552123366 1959 68655 5836 6298 597EX3 0390
JASA 1959 2 2520 45214 2233 5957 EX3 0400
JASA T1960 1 114.2502601 3931 2514125368 1960 69564 5723 6367 615EX3 0410
JASA 1960 2 2489 45850 2270 6250 EX3 0420
JASA 1961 1 115.7518173 4806 2572127852 1961 69331 5463 6388 662EX3 0430
JASA 1961 2 2594 45397 2279 6548 EX3 0440
JASA 1962 1 116.9554894 4007 2827130081 1962 70551 5190 6271 623EX3 0450
JASA 1962 2 2626 46652 2340 6849 EX3 0460
END EX3 0470
END EX3 0480
B0=0 BRNLEE BLOOD 1 1 1 11 51 EX4 0010
(A3,2I2,F5.0,F7.0) EX4 0020
PROBLEM FROM STATISTICAL THEORY AND METHODOLOGY BY BROWNLEE, EX4 0030
2ND EDITION, SECTION 11.4 . EX4 0040
Y = B(1)X1 EX4 0050
Y = RATES OF BLOOD FLOW EX4 0060
X = MEASUREMENTS BY AN INSTRUMENT EX4 0070
A B C D EX4 0080
1 1190. 1115. EX4 0090
2 1455. 1425. EX4 0100
3 1550. 1515. EX4 0110
4 1730. 1795. EX4 0120
5 1745. 1715. EX4 0130
6 1770. 1710. EX4 0140
7 1900. 1830. EX4 0150
8 1920. 1920. EX4 0160
9 1960. 1970. EX4 0170
10 2295. 2300. EX4 0180
11 2335. 2280. EX4 0190
12 2490. 2520. EX4 0200
13 2720. 2630. EX4 0210
14 2710. 2740. EX4 0220
15 2530. 2390. EX4 0230
16 2900. 2800. EX4 0240
17 2760. 2630. EX4 0250
18 3010. 2970. EX4 0260
END EX4 0270
B0=0 BB,SWITCHES=1 1 1 1 111111111 2 2 EX5 0010
Y IS CONSTANT 1 1 EX6 0010
1. 3. EX6 0020
2. 3. EX6 0030
3. 3. EX6 0040
3. 3. EX6 0040
4. 3. EX6 0050
5. 3. EX6 0060
6. 3. EX6 0070
7. 3. EX6 0080
8. 3. EX6 0090
9. 3. EX6 0100
END EX6 0110
VAR3 = VAR4 4 1 1 EX7 0010
(A6,I4,I2,3F6.3, T25, 2F6.3 ) EX7 0020
AUSTRL 1 124 33 8 646 EX7 0030
ASTRIA 2 49 31 6 355 EX7 0040
CANADA 3 181 38 8 631 EX7 0050
CEYLON 4 4 17 2 174 EX7 0060
CHILE 5 22 20 4 603 EX7 0070
DENMK 6 152 39 6 331 EX7 0080
FINLND 7 75 30 7 759 EX7 0090
FRANCE 8 54 29 7 282 EX7 0100
GMANY 9 43 35 6 316 EX7 0110
IRELND 10 41 31 5 490 EX7 0120
ISRAEL 11 17 23 4 457 EX7 0130
ITALY 12 22 21 3 282 EX7 0140
JAPAN 13 16 8 3 174 EX7 0150
MEXICO 14 10 23 3 269 EX7 0160
NTHLDS 15 63 37 6 240 EX7 0170
NWZEAL 16 170 40 8 525 EX7 0180
NORWAY 17 125 38 6 257 EX7 0190
PORTGL 18 15 25 4 240 EX7 0200
SWEDEN 19 221 39 7 331 EX7 0210
SWITZD 20 171 33 7 331 EX7 0220
UNKING 21 97 38 6 457 EX7 0230
U.S.A. 22 254 39 8 776 EX7 0240
END EX7 0250
2 VARIABLES PASS 1 3 1 1 1 211 121 1 EX8 0010
(6X, A4, I2, I1, F5.2, F6.2, F1.0, F10.4 ) EX8 0020
1 2 31 4 EX8 0030
EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1) EX8 0040
FITTED WITH Y = B0 + B1X1 + B2X2 EX8 0050
ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955. EX8 0060
1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2. EX8 0070
OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20. EX8 0080
STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS MUCH LESS EX8 0090
THAN RRMS OF FIT, SUGGESTING A BETTER FORM OF EQUATION IS NEEDED. EX8 0100
NEED FOR SQUARED TERM CAN BE SEEN FROM RESIDUAL VS. INDEPENDENT EX8 0110
VARIABLE X1 PLOT. SLIGHT EFFECT ON CURVATURE CAN BE SEEN FROM EX8 0120
COMPONENT AND COMPONENT-PLUS-RESIDUAL VS. INDEPENDENT VARIABLE X1 EX8 0130
PLOT. FROM "THE USE OF INDIVIDUAL EFFECTS AND RESIDUALS IN FITTING EX8 0140
EQUATIONS TO DATA" BY F.S.WOOD, TECHNOMETRICS VOL.15, NO 4, NOV. 1973. EX8 0150
X1 X2 Y EX8 0160
1 1 0.0 0.0 20.1640 EX8 0170
2 2 0.20 2.00 18.8470 EX8 0180
3 3 0.50 7.00 6.6780 EX8 0190
4 4 1.00 10.00 8.7090 EX8 0200
5 5 1.50 4.00 36.9340 EX8 0210
6 6 2.00 16.00 8.3970 EX8 0220
7 7 2.50 22.00 -1.7780 EX8 0230
8 8 3.00 6.00 53.1360 EX8 0240
9 9 3.50 9.00 51.8830 EX8 0250
1010 4.00 18.00 31.5640 EX8 0260
1111 4.50 28.00 5.7390 EX8 0270
1212 5.00 34.00 -6.4660 EX8 0280
1313 5.30 14.00 56.4940 EX8 0290
1414 5.50 24.00 28.5230 EX8 0300
1515 6.00 19.00 47.4980 EX8 0310
1616 6.50 38.00 -4.5750 EX8 0320
1717 7.00 33.00 10.7300 EX8 0330
1818 7.50 35.00 8.2140 EX8 0340
1919 7.80 30.00 23.7900 EX8 0350
2020 8.00 40.00 -3.5180 EX8 0360
121 0.0 0.0 20.2830 EX8 0370
222 0.20 2.00 16.9700 EX8 0380
323 0.50 7.00 8.3790 EX8 0390
424 1.00 10.00 9.8760 EX8 0400
525 1.50 4.00 37.7190 EX8 0410
626 2.00 16.00 8.4450 EX8 0420
727 2.50 22.00 -1.8410 EX8 0430
828 3.00 6.00 54.3390 EX8 0440
929 3.50 9.00 51.6460 EX8 0450
1030 4.00 18.00 30.7380 EX8 0460
1131 4.50 28.00 5.3730 EX8 0470
1232 5.00 34.00 -7.5370 EX8 0480
1333 5.30 14.00 53.9740 EX8 0490
1434 5.50 24.00 28.6360 EX8 0500
1535 6.00 19.00 46.0650 EX8 0510
1636 6.50 38.00 -6.3270 EX8 0520
1737 7.00 33.00 13.0010 EX8 0530
1838 7.50 35.00 7.8550 EX8 0540
1939 7.80 30.00 26.8690 EX8 0550
2040 8.00 40.00 -3.6590 EX8 0560
END EX8 0570
2 VARIABLES PASS 2 3 1 1 1 212 81 EX8 0580
8-4.0 1 2 9 1 1 32 4 EX8 0590
EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1) EX8 0600
FITTED WITH Y = B0 + B1(X1-4.0) + B2X2 + B3(X1-4.0)SQRD EX8 0610
ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955. EX8 0620
1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2. EX8 0630
OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20. EX8 0640
STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS CLOSE TO EX8 0650
RRMS OF FIT. EX8 0660
UNCODED FITTED EQUATION: Y = 20.006 + 20.310X1 - 3.007X2 - 1.038X1SQRD EX8 0670
X1-4.0 X2 X1SQRD Y EX8 0680